High-accuracy interferometric surface metrology is constantly gaining importance, not only in the classical area of optical fabrication, but also for new applications, such as magnetic disc flatness or semiconductor wafer flatness. Requirements for measurement resolution in the sub-nanometer range have become quite common. Of high importance is the slowly varying shape error, as well as the medium to high spatial frequency waviness of the surface under test. Achieving not only repeatability or reproducibility, but also absolute measurement accuracy for surface height measurements, with high spatial resolution, is difficult, since other applicable measurement techniques for calibration do not exist which are considerably more accurate than the interferometric test.
In the two-beam interferometers commonly used for testing, that is Fizeau-interferometer, Twyman-Green interferometer, or Mach-Zehnder interferometer, an illuminating beam is split into two beams. One beam, called the test beam, is directed to the surface under test, where it is reflected. The other beam, called the reference beam, is reflected at a reference surface. After recombination, the two reflected beams travel to a detector, usually a camera, where they interfere. The primary information contained in the resulting interferogram is then the phase difference between these two beams. Therefore, the shape of the test surface is not obtained independently, but only in combination with the reference surface. While the repeatability of the measurements can be extremely high, the measurement result of the test surface is only as accurate as the reference surface. If the reference surface deviations can be determined in a calibration step, they can be eliminated from the measurement. Then, the overall accuracy of the test surface map is limited by the accuracy of this calibration map.
The determination of a test surface independent of the reference surface is called an absolute measurement. Once one surface is absolutely known, it can act as a reference standard in subsequent interferometric tests, allowing for absolute testing. Thus, it is very desirable to have a technique available which provides an absolute surface deviation map without requiring any information about the shape of the other surfaces involved in the interferometric test.
The Fizeau interferometer configuration inherently is best suited for high accuracy testing, since the test beam and the reference beam are split by the last surface of the interferometer optics. The reference beam is reflected at this reference surface; and it is directed to the interferogram detector. The test beam is transmitted through the reference surface to the surface under test, from where it is reflected back to the interferometer and the interferogram detector. Consequently, all internal optical components of the interferometer are traversed by the test beam, as well as by the reference beam. These optical components are all in the common path of the two beams. Phase distributions resulting from the optics in the common path are the same for both beams. Consequently, these optics phase distributions drop out of the phase difference between the two beams. The only two surfaces which then are not in a common path are the reference surface and the test surface, and the interferogram phase is proportional only to the sum of both of these surface deviations.
The cancellation of the phase distributions due to the internal interferometer optics is strictly true only when the test beam and the reference beam travel on identical paths through the interferometer optics. This can only be the case when the test surface and the reference surface are identical, and are placed close to each other. Otherwise, a residual phase error, the so-called retrace error, due to the interferometer optics, is superposed on the measurement. Furthermore, in order to avoid difraction effects on the two beams interfering on the detector, the test surface has to be well imaged onto the interferogram detector. Thus, a highly accurate interferometric test requires that the surface deviations of the test surface are small, that the test and reference surfaces are aligned parallel to one another, and that the optical design of the interferometer optics minimizes re-trace errors.
Several techniques for absolute flatness testing have been described in the past; and they are listed below in the following articles: